Answer:
25
Step-by-step explanation:
Given
(-2 + 5i)/(4 + 3i)
Required
Multiply the denominator by 4 - 3i
The denominator of the fraction above is 4 + 3i
When multiplied by 4 - 3i, the result is as follows;.
Result = (4 + 3i)(4 - 3i)
Expand
Result = 4(4 - 3i) + 3i(4 - 3i)
Open both brackets (take it one at a time)
Result = 4 * 4 - 4 * 3i + 3i(4 - 3i)
Result = 16 - 12i + 3i(4 - 3i)
Open the second bracket
Result = 16 - 12i + 12i - 3i * 3i
Result = 16 - 12i + 12i - 9i²
In complex numbers, i = √-1
i² = (√-1)²
i² = √-1 * √-1
i² = -1
The expression
Result = 16 - 12i + 12i - 9i²
Becomes
Result = 16 - 12i + 12i - 9(-1)
Result = 16 - 12i + 12i + 9
Collect like terms
Result = 16 + 9 + 12i - 12i
Result = 25 + 0
Result = 25
Hence, when the denominator of the fraction is multiplied by 4 - 3i, the result is 25
